The value of x is 15.56.
Solution:
Tangent and Secant theorem:
If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.
BE = 22 BD = x, CD = x
BC = x + x = 2x
By the tangent and secant theorem,
Divide by 2 on both sides of the equation, we get
Take square root on both side of the equation.
x = 15.56
Hence the value of x is 15.56.
Answer:
Pan is closest to Paris when she gets to Florence when she is 35 miles away
Step-by-step explanation:
With Paris at (0,0), Rome is 40miles west which is on the negative x axis.
Florence is 35 miles closer (east to Paris) so we have -45 + 35 = -10
and 55 mikes north of Rome which is on the positive y-axis. So Florence is at point (-10,55)
The distance between the two points Florence and Paris is √(x2 - x1)^2 + (y2 - y1)^2
x1 = 0, y1 = 0
x2 = -10, y2 = 55
So we have
√(-10-0)^2 + (55-0)^2
= √(-10)^2 + (55)^2
= √ 100 + 3025
= √3125
= 55.9 mikes from Paris
Pam is closest to Paris when she gets to Florence when she is 35 miles away
